Both '～じゃない？' and '～(な)んじゃない？' exist, but have different nuances.
- '～じゃない？': The speaker already knows about or has made up his/her mind about something and is looking to convince the listener or confirm his/her understanding.
- ～(な)んじゃない？: The speaker is not sure about the statement, and is asking the opinion of the listener.
'～(な)んじゃない？' usually sounds softer and smoother, so might be a safer choice in most cases, but there are situations where only '～じゃない？' is correct:
(When scolding someone)
× もう言ったんじゃない？ (Did you or didn't you already tell him/her?)
○ もう言ったじゃない？ I already told you, don't you remember?
(When taking about Bush, and you already know when he became president)
× ブッシュが大統領になったのは2001年なんじゃない？ (Not wrong per se, but implies a genuine question, so doesn't fit here.)
○ ブッシュが大統領になったのは2001年じゃない？ Well, you know how Bush became president in 2001...
In the above cases, you're not really asking for the listener's opinion, so '～じゃない？' has to be used.
